Chapter 3

An animation of page 131: the equivalence of a concentric-with-epicycle (left) with an eccentric (right), and the difference encountered with the use of the apparent instead of the mean sun:

On the left, the center point is either the mean or the apparent sun.  If it be the mean sun, then the planet would be said to be the blue planet, positioned on a certain epicycle.  Were the center point the apparent sun, then the planet would follow the red course on a different epicycle.

On the right, rather than offsetting the planet, we instead use two different observers -- the blue mean sun and the red apparent sun -- with the planet moving on an eccentric.  If a planet actually moved in this way, uniformly and on a circle, both observers would develop equivalent conclusions respecting its motion, that is, they could both discover where the center of the circle of motion is, as well as its speed.